It is known that in brushes of a conventional type, particularly hair brushes, the strands or bristles are assembled on a support plate which is itself mounted on a support integral with the handle. In one known embodiment, the bristles are obtained from filaments folded in two; the two end legs of the loops thus formed are threaded into perforations previously made in the support plate and project from the front face of the plate to form the bristles of the brush. Thus, one filament yields two bristles and in general there are two filaments or four bristles provided for each perforation. For assembling the strands on the support plate, particularly when they are made from synthetic fibers, the loop-shaped portions of the filaments which are on the rear face of the plate are transformed by fusing or melting into balls which maintain the bristle in the perforation of the plate. The brush of the type described above, as well as most hair brushes which are currently used, have the disadvantage that the tip of these strands may present sharp edges liable to injure or irritate the scalp. Moreover, even if the tips of the strands are rounded, the risk of injury or irritation is not entirely eliminated, due to their small radius of curvature.